Geometry of tropical moduli spaces and linkage of graphs

Abstract

We prove the following "linkage" theorem: two p-regular graphs of the same genus can be obtained from one another by a finite alternating sequence of one-edge-contractions; moreover this preserves 3-edge-connectivity. We use the linkage theorem to prove that various moduli spaces of tropical curves are connected through codimension one.

Final version incorporating the referees corrections

References in corpus (5)

• Enumerative tropical algebraic geometry in R2
• On the tropical Torelli map
• Moduli spaces of rational tropical curves
• Algebraic and tropical curves: comparing their moduli spaces
• Combinatorics of the tropical Torelli map

Cited by in corpus (13)

• On the tropical Torelli map
• Tropical Amplitudes
• Algebraic and tropical curves: comparing their moduli spaces
• The universal tropical Jacobian and the skeleton of the Esteves' universal Jacobian
• Topology of the tropical moduli spaces $M_{2,n}$
• Tropical covers of curves and their moduli spaces
• Combinatorics of the tropical Torelli map
• A universal tropical Jacobian over $M_g^{\trop}$
• The automorphism group of $M_{0,n}^{\text{trop}}$ and ${\overline{M}}_{0,n}^{\text{trop}}$
• Tropical hyperelliptic curves
• Generic singular configurations of linkages
• Point Counts of D_k and Some A_k and E_k Integer Lattices Inside Hypercubes
• On tropical Clifford's Theorem